It simply depends on your choice weather you want to keep www or not. Just remember always fix 301 redirection of your website. Redirect your website either to www or with www by uploading a hta access file. If you don't fix redirection issue of your website there will be trouble. Cause a website with or without www is identical to human eye but they are totally different domains to SE. Search engine will think that these two domains are using same content and will penalize it.
There is actually no big difference in terms of optimizing websites and spreading the word about domains but since the good old standard for the web starts with www so it is suggested to use it. One important point to mention in this respect is trying to make a decision and then stick to it. For example, if you decide to use www. at the beginning of your site address, you should build links with www. in syntax too.
Sometimes when webmasters for example choose to use http:// instead of the www. at the beginning of their domains, they may mistakenly create lots of links having www. at the beginning and these changes in linking can cause problems. For example even if lots of new links are pointing to http:// part of a domain, but when you examine the www. area, you may not notice some PR impacts.